算式(1+1/2+1/3...+1/20)+(1+2/3+2/4+2/5..+2/20)+.+(1+18/19+18/2
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算式(1+1/2+1/3...+1/20)+(1+2/3+2/4+2/5..+2/20)+.+(1+18/19+18/20)+(1+19/20)
求结果!我算得220
求结果!我算得220
![算式(1+1/2+1/3...+1/20)+(1+2/3+2/4+2/5..+2/20)+.+(1+18/19+18/2](/uploads/image/z/15986936-56-6.jpg?t=%E7%AE%97%E5%BC%8F%281%2B1%2F2%2B1%2F3...%2B1%2F20%29%2B%281%2B2%2F3%2B2%2F4%2B2%2F5..%2B2%2F20%29%2B.%2B%EF%BC%881%2B18%2F19%2B18%2F2)
原式=(1/1+1/2+1/3+、、、+1/20)+(2/2+2/3+、、、+2/20)+、、、+(18/18+18/19+18/20)+(19/19+19/20)
=(1+2+、、、+19)/20+(1+2+、、、+18)/19+、、、+(1+2+3)/4+(1+2)/3+1/2+1*20
={(1+19)*19/2}/20+{(1+18)*18/2}/19+、、、+{(1+3)*3/2}/4+{(1+2)*2/2}/3+1/2+20
=19/2+18/2+、、、+3/2+2/2+1/2+20
=(1+2+3+、、、+19)/2+20
={(1+19)*19/2}/2+20
=19*5+20=115
=(1+2+、、、+19)/20+(1+2+、、、+18)/19+、、、+(1+2+3)/4+(1+2)/3+1/2+1*20
={(1+19)*19/2}/20+{(1+18)*18/2}/19+、、、+{(1+3)*3/2}/4+{(1+2)*2/2}/3+1/2+20
=19/2+18/2+、、、+3/2+2/2+1/2+20
=(1+2+3+、、、+19)/2+20
={(1+19)*19/2}/2+20
=19*5+20=115